Chaohui Chen

Distributed Gauss-Newton optimization method for history matching problems with multiple best matches

Minimizing a sum of squared data mismatches is a key ingredient in many assisted history matching (AHM) workflows. A novel approach is developed to efficiently find multiple local minima of a data mismatch objective function, by performing Gauss-Newton (GN) minimizations concurrently while sharing information between dispersed regions in the reduced parameter space dynamically. To start, a large number of different initial parameter values (i.e., model realizations) are randomly generated and are used as initial search points and base-cases for each subsequent optimization. Predicted data for all realizations are obtained by simulating these search points concurrently, and relevant simulation results for all successful simulation jobs are recorded in a training data set. A local quadratic model around each base-case is constructed using the GN formulation, where the required sensitivity matrix is approximated by linear regression of nondegenerated points, collected in the training data set, that are closest to the given base-case. A new search point for each base-case is generated by minimizing the local quadratic approximate model within a trust region, and the training data set is updated accordingly once the simulation job corresponding to each search point is successfully completed. The base-cases are updated iteratively if their corresponding search points improve the data mismatch. Finally, each base-case will converge to a local minimum in the region of attraction of the initial base-case. The proposed approach is applied to different test problems with uncertain parameters being limited to hundreds or fewer. Most local minima of these test problems are found with both satisfactory accuracy and efficiency.

Distributed Gauss-Newton Method for History Matching Problems with Multiple Best Matches

A novel assisted-history-matching (AHM) approach is developed to efficiently find multiple local minima of the objective function, by performing Gauss-Newton (GN) minimizations concurrently and and sharing information from dispersed regions in parameter space dynamically. To start, a large number of different initial parameter values (i.e., model realizations) are randomly generated and are used as base-cases for each realization. Production data for all realizations are obtained by simulating these base-cases concurrently. A local quadratic model around each base-case is constructed using the GN formulation, where the required sensitivity-matrix is approximated by linear interpolation of non-degenerated points that are closest to the given base-case. New search points are generated by minimizing the local quadratic approximate models. The base-cases are updated iteratively if their corresponding search points improve the data mismatch. Finally, each base case will converge to a local minimum in the vicinity of the initial base-case. The proposed approach is applied to different test problems. Most local minima of these test problems are found with satisfactory accuracy. Compared to traditional AHM approaches using derivative-free optimization algorithms using multiple initial start values, the propose approach may achieve a reduction factor in computer resource usage that is proportional to the number of parameters.

An Improved Inversion Workflow Jointly Assimilating 4D Seismic and Production Data

Description: Quantitative integration of 4D seismic data with production data into reservoir models is a challenging task. This paper tackles two key issues of the complex joint inversion workflow to improve its efficiency and accuracy. We applied two derivative free optimization (DFO) methods, namely particle swarm optimization (PSO) and Simultaneous Perturbation and Multivariate Interpolation (SPMI), and compared their performances. We tested different strategies of effectively mining information in both 4D seismic and production data. We proposed a method of choosing the different weights in data domain by utilizing sensitivity of inversion parameters to different types of data. We also tested the strategy of combining the inversion results from separate inversion runs using 4D seismic data or production data only. Application: We tested the workflow in a 3D synthetic model. Uncertain parameters for this model include relationship between porosity and permeability, and the ratios of kv to kh for different reservoir zones. The performance of PSO and SPMI are compared in terms of the evolution of objective function and estimation of uncertain parameters. We also provide recommendations about when to use which method. Different strategies of optimal use of 4D seismic and production data are also applied and compared using this model. The learning is also applied to a deepwater turbidite field. Results, Observations, Conclusions: Both PSO and SPMI are effective DFO methods and deliver good results for 4D seismic history matching problems. The complementary features of these two methods can ensure both applicability and efficiency of this joint inversion workflow. Choosing proper weights in either data or model domain can improve the accuracy of this workflow. Significance of Subject Matter: By solving the two key issues of jointly assimilating 4D seismic and production data, we deliver reliable workflow for reservoir model characterization and management.